My FIL's secret sauce is

½ cup mayonnaise
½ cup ketchup
few dashes Texas Pete hot sauce (like Louisiana hot sauce)

few dashes juice from pickled hot peppers

But in a pinch he would mix cocktail sauce and tartar sauce in equal parts.
The pickled hot peppers are just hot peppers soaked in vinegar in the refrigerator indefinitely.

Many years ago I worked at a restaurant and they just used to mix Worcestershire Sauce, Tomato Sauce, and Vanilla Ice-cream. No set amounts just enough to do the number of people at the time, and taste it and add a bit more of whatever it needs, eg.. more colour, add a bit more tomato sauce, or more kick, add more Worcestershire etc.....Stir it in a little dish until it tastes just as you want. You always have those ingredients around, and it's quick and easy. I am Australian and the ketchup we get here is a bit strong and most people use tomato sauce on pies etc.